Sheets (2-0), who tossed six scoreless innings Sunday in his first start in since 2010 elbow ligament replacement surgery, repeated the performance Saturday, blanking the Nationals over six frames.
The former Milwaukee Brewers ace allowed five hits and walked three while striking out six.
The Braves turned three double plays en route to the win -- their second straight over National League East-leading Washington.
Kris Medlin contributed two scoreless innings and Chad Durbin completed the shutout for second-place Atlanta, which pulled to within 1 1/2 games of the NL East top spot.
Edwin Jackson (5-6) absorbed the loss despite yielding only one run on five hits over seven full frames for the Nationals.